However, Coyle insists defender Gary Cahill will not be part of any package after he had been linked with the Gunners.
'I called Arsene Wenger to thank him for letting us have Jack last season. I think it was a fantastic experience for him and a very worthwhile one for us too,' said Coyle.
Come back, Jack: Bolton want to resign Wilshere after the youngster enjoyed a successful loan stint at the Reebok
'I honestly think he improved as a player, so we have asked the question. If he feels that Jack is not quite ready for first-team football [at Arsenal] next season, then we would love the opportunity to bring him back.
'The fans can see what a great young English talent he is, and I believe that with another full season under his belt, that he can really push on.
'That is how we left it - so we'll both go away and take a break, and then see what happens.'
Staying put: Bolton boss Owen Coyle says defender Gary Cahill isn't going anywhere this summer
Coyle is confident defender Gary Cahill will not be leaving the Reebok this summer despite a host of interest from big clubs such as Manchester United and Arsenal.
'There has been no dialogue about Gary Cahill whatsoever, with Arsenal or anyone else for that matter,' Coyle added in the Bolton News.
'I have got no desire to lose Gary - he's a big, big part of what I am trying to do here.'
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